Below is the same structured explanation, now focused only on dominant 7♭5 chords generated from F°7, staying strictly within the Barry Harris framework.
Developing Dominant 7♭5 Chords from F°7
In the Barry Harris system, a dominant 7♭5 chord is created by altering two non-consecutive notes of a fully diminished seventh chord (either raised or lowered by a half-step).
Non-consecutive notes are F – B, A♭– D
Because the diminished chord is symmetrical, F°7 can generate four different dominant 7♭5 chords, all related by minor thirds.
Starting point
F°7
Notes: F – A♭– B – D (E♭♭)
1. Lower D → D♭ and A♭→ G → G7♭5 and D♭7♭5
G – B – D♭– F
D♭– F – G (A♭♭) – B (C♭)
This produces G7♭5 and D♭7♭5
2. Raise D → E♭ and A♭→ A → B7♭5 and F7♭5
B – E♭– F – A
F – A – B – E♭
This produces B7♭5 and F7♭5
3. Lower B → B♭ and F → E → E7♭5 and B♭7♭5
E – A♭(G) – B♭– D
B♭– D – E – A ♭
This produces E7♭5 and B♭7♭5
4. Raise F → F♯ and B → C → D7♭5 and A♭7♭5
D – F♯ – A♭ – C
A♭– C – D – F♯ (G♭)
This produces D7♭5 and A♭7♭5
What This Shows
Each dominant ♭5 chord:
Comes from two non-adjacent diminished notes resolving
Retains two notes of the original diminished chord
Sits between a regular dominant and full diminished tension
Barry Harris used the dominant ♭5 sound as a way to intensify dominant motion without breaking the internal logic of the diminished chord.